Finite Group Databasebeta

← C2×#13072106 #14921903

Subgroups — C2×#13072106 #14921903

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13072106C2116yesmaximal, direct product factor
4C2×#10622566C212yesmaximal, complemented
5C2×#10622574C212yesmaximal, complemented
6C2×#10622598C211yesmaximal, characteristic, complemented
7C2×#10622571C212yesmaximal, complemented
8C2×#10622549C211yesmaximal, characteristic, complemented
9C2×#10622556C212yesmaximal, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C24×Dic11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×#66991—28no—
24C2×#66991C2218yes—
25C2×D4×Dic11—28no—
26C2×D4×Dic11C2218yescomplemented
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34C11×#390C2218yescomplemented
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622600C2218yescomplemented
42#10622598C2218yescomplemented
43#10622574C22116yescomplemented
44#10622571C22116yescomplemented
45#10622566C22116yescomplemented
46#10622556C22116yescomplemented
47C4×(C2×D11)⋊C4C2218yescomplemented
48#10622549C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11D418yes—
54C22×D4×C11C2314yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11C2318yes—
63C23×Dic11—28no—
64C23×Dic11—28no—
65C23×Dic11—44no—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2318yes—
71C23×Dic11C2311yescharacteristic
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11C2314yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4C2318yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C42×C11—24no—
83C2×C42×C11C2314yes—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88#66991—232no—
89D4×Dic11—232no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11—44no—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2318yes—
102C2×C4×Dic11—24no—
103C2×C4×Dic11C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C2×#2420—111nomaximal, Sylow
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11C2×D418yes—
118C24×C11C2414yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11#4114yes—
127C23×D11C2412yes—
128C2×D4×C11—232no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11C2×D4116yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D414yes—
142C22×C4×C11#4114yes—
143C22×C4×C11#4114yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C2×C22⋊D11—216no—
149C2×C22⋊D11—216no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—432no—
152C22×Dic11—216no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—216no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—48no—
169C22×Dic11—432no—
170C22×Dic11#4114yes—
171C22×Dic11C2412yes—
172C22×Dic11C2414yes—
173C22×Dic11C2414yes—
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C2×C4×D11—28no—
177C2×C4×D11—28no—
178C2×C4×D11—28no—
179C2×C4×D11—416no—
180C11×C4⋊C4—28no—
181C11×C22⋊C4—48no—
182C11×C22⋊C4—48no—
183C42×C11—28no—
184C22⋊Dic11—216no—
185C22⋊Dic11—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—28no—
190C4⋊Dic11—28no—
191C4⋊Dic11—48no—
192C4×Dic11—28no—
193C22×#121—111no—
194C22×C4×D4—111no—
195#2420—1116no—
196C2×#397—112no—
197C2×#394—112no—
198C2×#390D1111yescharacteristic, complemented
199C2×#389—111no—
200C2×#386—112no—
201C2×#382—111no—
202C2×#381—112no—
203C2×#380—111no—
204C2×C4×C22⋊C4—111no—
205C23×C11—216no—
206C23×C11—216no—
207C23×C11—216no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11C22×D418yes—
219C23×C11C22×D412yes—
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C11C2511yescharacteristic
227C22×D11—28no—
228C22×D11—28no—
229C22×D11—28no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11C2×#4114yes—
241D4×C11—232no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—48no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11#123116yes—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2×#4114yes—
258C22⋊D11—432no—
259C2×Dic11—28no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—432no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11—48no—
278C2×Dic11—48no—
279C2×Dic11C2×#4114yes—
280C4×D11—416no—
281C23×D4—112no—
282C23×D4C2×D1111yescharacteristic
283C24×C4—112no—
284C24×C4—111no—
285C2×#121—118no—
286C2×#121—228no—
287C2×C4×D4—118no—
288C2×C4×D4—228no—
289C22×C4⋊C4—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4—112no—
292C22×C4⋊C4C2×D1111yescharacteristic
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4C2×D1112yes—
299C22×C22⋊C4C2×D1112yes—
300C22×C42—111no—
301C22×C42C2×D1111yescharacteristic
302#397—1116no—
303#394—1116no—
304#390C2×D1118yescomplemented
305#389—118no—
306#386—1116no—
307#382—118no—
308#381—1116no—
309#380—118no—
310C4×C22⋊C4—118no—
311C2×#95—112no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—111no—
316C2×#95—112no—
317C22×C11—28no—
318C22×C11—28no—
319C22×C11—28no—
320C22×C11—44no—
321C22×C11—432no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11C2×#12314yes—
326C22×C11#52914yes—
327C22×C11#54014yes—
328C22×C11#54614yes—
329C22×C11#54614yes—
330C22×C11#55314yes—
331C22×C11#55514yes—
332C22×C11C23×D411yescharacteristic
333C22×C11C22×#4111yescharacteristic
334C22×C11C22×#4111yescharacteristic
335C22×C11C22×#4111yescharacteristic
336C22×C11C22×#4111yescharacteristic
337C22×C11C2×H(5,𝔽2)11yescharacteristic
338C22×C11C2×H(5,𝔽2)11yescharacteristic
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—42no—
343C2×D11—416no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C4×C11—44no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11C2×#12318yes—
351Dic11—24no—
352Dic11—42no—
353Dic11—42no—
354Dic11—44no—
355Dic11—44no—
356C25—111no—
357C25C22×D1112yes—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—118no—
361C22×D4—228no—
362C22×D4—228no—
363C22×D4—444no—
364C22×D4D4418yes—
365C22×D4C22×D1114yes—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—112no—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—118no—
372C23×C4—114no—
373C23×C4—228no—
374C23×C4—228no—
375C23×C4—224no—
376C23×C4—224no—
377C23×C4—224no—
378C23×C4—444no—
379C23×C4C22×D1112yes—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383#121—2232no—
384C4×D4—2232no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—118no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4—444no—
392C2×C4⋊C4C22×D1114yes—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—228no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4C22×D1118yes—
406C2×C22⋊C4C22×D1118yes—
407C2×C42—24no—
408C2×C42—114no—
409C2×C42—224no—
410C2×C42C22×D1114yes—
411#95—114no—
412#95—114no—
413#95—118no—
414#95—118no—
415#95—118no—
416#95—118no—
417C2×C11—48no—
418C2×C11#242018yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#52911yescharacteristic
421C2×C11C2×#54011yescharacteristic
422C2×C11C2×#54611yescharacteristic
423C2×C11C2×#54611yescharacteristic
424C2×C11C2×#55311yescharacteristic
425C2×C11C2×#55511yescharacteristic
426D11—44no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—114no—
434C24—112no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24C2×D4418yes—
442C24C23×D1114yes—
443C24C23×D1111yescharacteristic
444C2×D4—232no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—2216no—
448C2×D4—2216no—
449C2×D4—448no—
450C2×D4—4432no—
451C2×D4C2×D44116yes—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—114no—
462C22×C4—112no—
463C22×C4—112no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—2216no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—2216no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—448no—
487C22×C4—4432no—
488C22×C4—4416no—
489C22×C4C2×D4414yes—
490C22×C4#434114yes—
491C22×C4#434114yes—
492C22×C4C23×D1112yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C4⋊C4—28no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—228no—
503C22⋊C4—228no—
504C22⋊C4—2216no—
505C22⋊C4—2216no—
506C22⋊C4—448no—
507C42—28no—
508C42—228no—
509C11C2×#242011yescharacteristic, complemented, Sylow
510C23—216no—
511C23—216no—
512C23—216no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—114no—
524C23—228no—
525C23—228no—
526C23—222no—
527C23—222no—
528C23—222no—
529C23—222no—
530C23—222no—
531C23—222no—
532C23—228no—
533C23—444no—
534C23—444no—
535C23—444no—
536C23—444no—
537C23C22×D4418yes—
538C23C22×D4412yes—
539C23C2×#434112yes—
540C23C2×#434112yes—
541C23#6703712yes—
542C23#6703712yes—
543C23#41×D1112yes—
544C23#41×D1112yes—
545C23C24×D1111yescharacteristic
546D4—232no—
547D4—4432no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—48no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—114no—
561C2×C4—228no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—4432no—
577C2×C4—444no—
578C2×C4—448no—
579C2×C4—448no—
580C2×C4—444no—
581C2×C4—4416no—
582C2×C4#66939116yes—
583C2×C4C22×D4414yes—
584C2×C4C2×#434114yes—
585C2×C4C2×#434114yes—
586C22—28no—
587C22—28no—
588C22—28no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—432no—
594C22—224no—
595C22—224no—
596C22—224no—
597C22—442no—
598C22—442no—
599C22—442no—
600C22—4416no—
601C22—442no—
602C22C2×#6693914yes—
603C22#1062308514yes—
604C22#1062308514yes—
605C22#1062314514yes—
606C22#1062314714yes—
607C22#1062321114yes—
608C22#1062325014yes—
609C22C23×D4411yescharacteristic
610C22C22×#434111yescharacteristic
611C22C22×#434111yescharacteristic
612C22C2×#6703711yescharacteristic
613C22C2×#6703711yescharacteristic
614C22C2×#41×D1111yescharacteristic
615C22C2×#41×D1111yescharacteristic
616C4—42no—
617C4—42no—
618C4—44no—
619C4—224no—
620C4—444no—
621C4—444no—
622C4—442no—
623C4—442no—
624C4C2×#6693918yes—
625C2—48no—
626C2—444no—
627C2#1307210618yesdirect product factor
628C2C22×#6693911yescharacteristic
629C2C2×#1062321111yescharacteristic
630C2C2×#1062325011yescharacteristic
631C2C2×#1062308511yescharacteristic
632C2C2×#1062308511yescharacteristic
633C2C2×#1062314511yescharacteristic
634C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#390D11
hypocenterC11C2×#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×D4×Dic11C2semidirect
3. #13072106C2direct (N × H)
4. C2×#10622566C2semidirect
5. C2×#10622574C2semidirect
6. C2×#10622598C2semidirect
7. C2×#10622571C2semidirect
8. C2×#10622549C2semidirect
9. C2×#10622556C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C2×C11×#390C2semidirect
26. C2×D4×Dic11C22semidirect
34. C11×#390C22semidirect
41. #10622600C22semidirect
42. #10622598C22semidirect
43. #10622574C22semidirect
44. #10622571C22semidirect
45. #10622566C22semidirect
46. #10622556C22semidirect
47. C4×(C2×D11)⋊C4C22semidirect
48. #10622549C22semidirect
198. C2×#390D11semidirect
304. #390C2×D11semidirect
418. C2×C11#2420semidirect
509. C11C2×#2420semidirect
627. C2#13072106direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669912
C22×D4×Dic112
#130721062
C2×#106225662
C2×#106225742
C2×#106225982
C2×#106225712
C2×#106225492
C2×#106225562
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3902
C2×#242011